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As a prefatory remark, I should make clear that I don't understand the mathematics in your question.

However, one problem which has already been mentioned is that readers who understand measure theory are nevertheless unable to understand the terminology of the question. The same applies to this meta-question: what do you mean by "the leading question"? If you mean the primary / principal question then I would suggest that asking only one question should simplify the post.

Secondly, in any long mathematical text it's useful for understanding to front-load the high-level view rather than diving into a detailed example of a preliminary before we know what we should focus on.

Thirdly, although in principle the scope of MCD includes research-level questions, in practice you're more likely to get answers to this level of question on MathOverflow.

On a related note, although it doesn't directly answer this meta-question, if your follow-up questions are attempts to specialise the original question in the hope that the specialisations will be easier to understand then it would be useful to interlink them and explain the relationships.